In Praise of K-class Stars

byPaul GilsteronAugust 12, 2009

When it comes to exoplanet speculations, we’re still in the era when data are few and dominated by selection effect, which is why we began by finding so many ‘hot Jupiters’ — such planets seem made to order for relatively short-term radial velocity detections. It’s a golden age for speculation, with the promise of new instrumentation and a boatload of information from missions like Kepler and CoRoT to be delivered within a few years. What an extraordinary time to be doing exoplanetary science.

The big questions can’t be answered yet, but it shouldn’t be long before we have an inkling about what kind of stars are most likely to produce terrestrial planets. And maybe a qualification is in order. M-dwarfs are so common in our galaxy — some estimates run to seventy percent of all stars and up — that finding habitable worlds around them would hugely increase the possible venues for life. But is there any way we could call planets around M-dwarfs ‘Earth-like?’ Maybe in terms of temperature in a specific habitable zone on the surface, but little else applies.

M-dwarfs vs. the Early Sun

An M-dwarf planet in the habitable zone is, around many such stars, going to be subject to the kind of solar flare activity that could either prevent life from gaining a foothold altogether, or else serve as an evolutionary stimulus. Either way, conditions like this don’t seem Earth-like, even if the early Earth was subjected to its own barrage of harsh ultraviolet radiation before life forms could produce enough oxygen to yield an ozone layer. Rocco Mancinelli (SETI Institute) talked about this at the recent IAU Symposium on Solar and Stellar Variability — Impact on Earth and Planets. Here he discusses the importance of UV:

“We also see ultraviolet radiation as a kind of selection mechanism. All three domains of life that exist today have common ultraviolet protection strategies such as a DNA repair mechanism and sheltering in water or in rocks. Those that did not were likely wiped out early on.”

Clearly, intense ultraviolet can’t be considered prohibitive to life. But again, that’s from Earth’s history around a G-class star. In addition to their flare activity, M-dwarf planets are likely to be tidally locked, producing weather patterns that will keep meteorologists up nights and probably reducing habitable zones to specific areas on the Sun side. Life may well be possible, but even if Kepler turns up M-dwarf rocky worlds in large numbers, we’ll be talking about conditions that are only marginally like Earth, though obviously with an astrobiological fascination all their own. What we may one day find living on such worlds should be exotic creatures indeed.

The Case for K-class Stars

Recently we’ve been kicking around the subject of K-class stars in the comments to various posts here, and with K stars we really can start talking about planets much more like our own. Here I fall back to the IAU meeting, where Jean-Mathias Grießmeier (ASTRON, The Netherlands) looked at the role of magnetic fields in determining how likely life is to develop. Such fields provide a shield against incoming charged particles from stellar mass ejections as well as pervasive solar winds. They also offer protection against high-energy cosmic rays.

And here’s the quote from Grießmeier that resonates with me. He’s looking at the kind of stars we might expect to find life around, and concludes that our Sun probably wouldn’t top a list of such stars as compiled by the average extraterrestrial astronomer:

“The Sun does not seem like the perfect star for a system where life might arise. Although it is hard to argue with the Sun’s ‘success’ as it so far is the only star known to host a planet with life, our studies indicate that the ideal stars to support planets suitable for life for tens of billions of years may be a smaller slower burning ‘orange dwarf’ with a longer lifetime than the Sun ― about 20-40 billion years. These stars, also called K stars, are stable stars with a habitable zone that remains in the same place for tens of billions of years. They are 10 times more numerous than the Sun, and may provide the best potential habitat for life in the long run.”

K stars — now we’re talking! A stable habitable zone that offers a long period for life’s development, and a population that far outnumbers G-class stars like the Sun. It’s nice to speculate about the closest such star, the K-dwarf Alpha Centauri B, but of course we still have to resolve the question of planetary formation in binary systems like this one. We should have some answers fairly quickly, what with two ongoing attempts to find planets in the Alpha Centauri system, and may well know about Centauri planets before we start getting hard returns from Kepler.

Describing a Life-Bearing Planet

What does Grießmeier lean to when it comes to planets that would make good astrobiological candidates? Planets more massive than the Earth by two or three times, where higher gravity can make it easier to retain the atmosphere, and a larger liquid iron core offers robust magnetic field protection. The clincher here is the slower cooling of such a planet, allowing it to keep that magnetic protection for longer periods.

Meanwhile, Manfred Cuntz (University of Texas, Arlington) told the IAU meeting about his own team’s work on ultraviolet radiation and its effect on DNA. This is also quite interesting:

“The most significant damage associated with ultraviolet light occurs from UV-C, which is produced in enormous quantities in the photosphere of hotter F-type stars and further out, in the chromospheres, of cooler orange K-type and red M-type stars. Our Sun is an intermediate, yellow G-type star. The ultraviolet and cosmic ray environment around a star may very well have ‘chosen’ what type of life could arise around it.”

So many life factors, and so many stars to study! More in this IAU news release, which also looks at Edward Guinan’s work at Villanova, where he’s been studying stars that are analogues to the Sun at various stages of their life cycles. Among the findings: The Sun rotated ten times faster four billion years ago than it does now, thus producing a far stronger magnetic field. Our young Sol emitted X-rays and ultraviolet radiation several hundred times stronger than the Sun does today.

Comments on this entry are closed.

FrankHAugust 12, 2009, 15:36

I think the biggest problem with K stars is the width of their HZ. A star with half the Sun’s luminosity is going to have a HZ about 1/2 as wide (assuming the Sun’s HZ goes from around 1AU to 1.6AU).

Let’s not get carried away here. K dwarfs later than K5 are probably going to have the same tidal locking problems that M dwarfs have.

To give an example that’s close at hand, Epsilon Indi is a K4.5 dwarf, right in the middle of the Ks. It has about 0.75 solar masses but is only about 0.17 as luminous as the Sun. So a planet would have to orbit at around 0.42 aus in order to get as much insolation as Earth. As it happens, that’s right around the point where a terrestrial planet will tidally lock within a few billion years or less.

So, Epsilon Indi is borderline… but anything less luminous is probably out.

Note that the time required for tidal locking is inversely proportionate to the mass of the planet, inversely proportionate to the mass of the star squared… and directly proportionate to the sixth (!) power of the orbital radius. So, half the orbital radius, get locking 64 times as fast.

The locking time for Earth is estimated as being roughly-on-the-order-of 100 billion years, give or take. So, once you get inside 0.5 au, things start to get dubious, and by the time you’re at 0.4 au, even around a somewhat less massive star, you’re almost certainly locked long before complex life can evolve.

Not to rain on the parade; the early Ks do indeed look interesting, and there are several in our neighborhood — Epsilon Eridani, Sigma Draconis, and of course Alpha Centauri B. We should be looking at them closely, sure. I’m just saying.

Absolute width of the habitable zone is not such a problem. Closer to the star the planetary orbits can be packed together more tightly, so the probability of a planet being in the HZ is not going to be too greatly affected (note for example that the two gas giants orbiting Gliese 876 are both in the habitable zone, at least by some definitions of the HZ extent). On a logarithmic scale, the habitable zone is the same width.

All well and good, but I’d like more data on exactly how deleterious tidal locking might be to biospheres before I ditched the late Ks and Ms. There have been wildy contradictory papers released about that in recent years.

Ms themselves span a huge range of masses and luminosities, and I believe the early Ms are not fully convective, which presumably has an influence on their flare propensity.

Lets wait and see (having said that, wouldn’t some news about Alpha Cen B be amazing)!

If we’re looking for a compromise between “being Sunlike” and “spending more time on the main sequence”, then don’t the late Gs look as good or better than the Ks?

A late G would have 0.8-0.9 solar masses and between 1/3 and 2/3 the Sun’s luminosity. Tidal locking wouldn’t be an issue in the habitable zone. And their main sequence lifespans would be about double that of the Sun’s. ~20 billion years seems like a reasonable time to get complex life up and running.

Abundance is an issue. There are seven late Gs within 10 parsecs of the Sun, as compared to 29 early Ks; if that’s typical, then early Ks are about four times as common as late Gs.

BTW, Grießmeier’s comment about “they are ten times more numerous than the Sun” seems a slight exaggeration. Going back to the “dwarfs within 10 parsecs of the Sun”, there are 12 G Vs (counting the Sun itself) and 38 K Vs. That’s more like three times more numerous.

Sure, the sample size (50 stars) is an issue; the region around the Sun seems a little richer in early Gs, and poorer in late Ks, than you might expect. But I suspect that in our region of the galaxy generally, we’re talking four or five to one, not ten to one.

@Frank H: though the HZ will indeed be narrower for lower luminosity (K) stars, the relationship is not linear (at least not as HZ is defined by liquid water and correllated required insolation), since insolation is inversely proportionate with the square of distance (i.e. double the distance -> 1/4 of insolation, half the distance -> 4 times insolation).
Hence I expect a half solar lum. K star to have a somewhat narrower HZ, however not half solar but a bit more than that. And, as adny points out, the big advantage is the long-term stability of their HZ.

I agree with Doug that the early K stars seem the most promising from point of view of luminosity and tidal locking. For these reasons and the tidal locking correllations mentioned by Doug, I would rather limit it to even earlier K, maybe K2 or K3 (with a luminosity of at least 0.25 solar). Or even earlier: a ‘typical’ latest G/earliest K (K0) star with 0.45 – 0.5 solar lum. would experience about earthlike insolation at about Venusian distance (0.7 AU). At such a distance it would, according to Doug’s correllations, take some 12 gy for an earthlike planet to get tidally locked.
And also include the later G stars (roughly from G5)!

Quote from article:
“They are 10 times more numerous than the Sun”
This quote seems quite meaningless, what exactly does it mean, comparing apples and oranges (whole K class against subclass G2? Logically then).

If we make a fair comparison, whole K against whole G, we can tell from the RECONS, NStars and Hipparcos databases, that the difference in abundance is (not surprisingly) significant, but not that extreme: K stars are just over double (about 2.3 times) as abundant as G stars.

If, I think more interestingly, we compare two subgroups of solar type stars (often defined as F7 through K2, subdivided in the two groups F7 – G4 and G5 – K2), we find that the later solar type stars (G5 – K2) are about 1.6 to 1.8 times as abundant as the earlier (F7 – G4), again significant but not that extreme.

Abstract: 11 UMi and HD 32518 belong to a sample of 62 K giant stars that has been observed since February 2004 using the 2m Alfred Jensch telescope of the Th\”uringer Landessternwarte (TLS) to measure precise radial velocities (RVs).

The aim of this survey is to investigate the dependence of planet formation on the mass of the host star by searching for planetary companions around intermediate-mass giants. An iodine absorption cell was used to obtain accurate RVs for this study.

Our measurements reveal that the RVs of 11 UMi show a periodic variation of 516.22 days. The RV curve of HD 32518 shows sinusoidal variations with a period of 157.54 days. The HIPPARCOS photometry as well as our H\alpha core flux measurements reveal no variability with the RV period. Thus, Keplerian motion is the most likely explanation for the observed RV variations for both giant stars.

An exoplanet with a minimum mass of 10.5 Jupiter masses orbits the K giant 11 UMi. The K1 III giant HD 32518 hosts a planetary companion with a minimum mass of 3.0 Jupiter masses in a nearly circular orbit. These are the 4th and 5th planets published from this TLS survey.

Assuming the logarithmic rule about rotationally locked planets is correct, we would assume that any HZ smaller than 0.5 AU is going to lead to a tidally locked planet within, say, a 5-6 billion year period. This sets the lower bound on stellar size. Our sun sets the upper bound. So, we look at starts from G2 on down to about K5. Even though the K range is more limited than the G range, there are probably twice as many K’s as G’s. So, we’re still looking mostly at K’s.

Recent papers suggest that tidally locked planets could still be habitable. However, they would not be very Earth-like. If they are water worlds, the ocean currents should effectively distribute the heat around the planet such that there is not too much of a differential between the day side and the night side of the planet. However, if the planet is dry, the temperature extremes between the day and night side are likely to be extreme. In any case, a tidally locked planet is not going to be very Earth-like in having a day-night cycle. The twilight zone of such a planet is the only area that is likely to actually be a comfortable place to live.

With regards to the smaller K’s and M’s, there is a size range where a planet in the HZ will be tidally locked, but still far enough away from the star that the flares do not cause too much trouble to the planet and its atmosphere and where the solar wind is weak enough that it does not carry away the planet’s atmosphere. Perhaps the range of stars that meet this specification is from K5 down to, say, M3 or M4.

With a mid K star, you may have the HZ planet where it is not tidally locked, but where the rotation period is say 1 or 3 Earth weeks long. This would still result is some wild day/night temperature fluctuations.

If we make a fair comparison, whole K against whole G, we can tell from the RECONS, NStars and Hipparcos databases, that the difference in abundance is (not surprisingly) significant, but not that extreme: K stars are just over double (about 2.3 times) as abundant as G stars.

Is that before or after correcting for bias due to luminosity? This will have implications for completeness of the results.

K stars have longer lifespans, but narrower habitable zone, which is bad for two reasons. First, is of course lower chance that a planet happens to be there. Second, that because the star increases luminosity, the habitable zone moves outwards, and narrower zone means that if you started on the outer edge, the inner edge will close in on you faster. This is of course countered by slower motion of the habitable zone, but which effect is stronger I don’t know. I didn’t do the maths yet.

Doug,
Don’t lets forget that there other ways than just insolation to maintain habitable temperatures. A planet receiving 0.17 of Earth’s insolation would maintain an average surface temperature of 288K through adiabatic warming if it had approximately 5 bar surface pressure (assuming the bulk of of atm. was Nitrogen.)

@andy: yes, some correction for luminosity: only main sequence (V and border cases IV-V), only above 0.2 and below 3 solar lum. If we reduce the upper limit to 2 solar, the ratio becomes more in favor of K (and more in favor of the late G plus early K against late F plus early G), but still not above 3 (resp. 2.5).

“Recent papers suggest that tidally locked planets could still be habitable. However, they would not be very Earth-like. ”

If our focus is on finding worlds that can harbor alien life and not just
Earth-type planets we can colonize some day, then I hope we will pursue
finding and studying worlds around K-class stars and other places that
might have life, just not the kind we are used to.

At 20 to 40 Gy, and ten times more numerous than stars like the Sun, I can only imagine how advanced any future ETI and future human civilizations around such stars could become during the life time of such stars.

It truely boggles the mind when we realize that the human race has been in the making for a few million years now starting with our early hominid ancestors, and just thinking of the technology we have developed in the past 100 years.

I can imagine some future vantage point where some of our descendents look up into the sky at noon to see an orange sun instead of a yellow dwarf like our sun.

From the RECONS, NStars and Hipparcos databases, I count some 7 main sequence (V) G9/K0 stars up to 50 ly. However, the number increases to about 20, if you include G8 and K0/K1 bordercases, different databases sometimes give different spectral subtypes. It corresponds with roughly 0.35 to 0.50 solar luminosity.

Since (MS) lifespan is correllated with mass and inversely so with luminosity, I expect that a typical K0 (like Alpha Centauri B, of Tau Ceti, although the latter is often classified as G8/G9) with 0.85 Msol and 0.45 Lsol would have a main sequence lifespan of almost twice that of our sun.

I was intrigued by the post of Doug M. August 12, 2009 at 17:10, and in particular by the tidal locking formula and its consequences, so I did some additional calculating, assuming besides the given formula and well-known distance/luminosity correllation, that;
a) the locking time for Earth is about 100 gy (I got the impression from some other sources that it may actually be considerably shorter, rather 60 gy orso);
b) the habitable lifespan (hablife) for earth is about 5.5 gy;
c) main sequence lifespan and hablife span of main sequence stars are both proportionate with the mass of the star and inversely so with its luminosity;
d) the favorable midpoint of the earth’s continuously habitable zone (CHZ) is not at 1 AU but at 1.2 AU (earth seems to be rather close to the inner edge of the CHZ right now, this edge being at about 0.95 AU);

The results were rather sobering: even assuming the (very) generous 100 gy for the earth’s tidal locking and the equally (possibly too) generous 1.2 AU as the midpoint of our own CHZ, an earthlike planet orbiting a star below about 0.20 Lsol, 0.5 AU (roughly corresponding with K2/K3) gets tidally locked so quickly that, though life may have time to arise, it won’t have much time left to develop before tidal locking starts kicking in.

In fact, anything below about 0.25 to 0.3 Lsol, 0.6 – 0.65 AU (roughly corresponding with K1/K2), is hardly worthwhile from a perspective of the advantage of long stable lifespan of K-stars, because the locking time will hardly or not be sufficient to bridge the expected habitable life span of 12 – 14 gy, in other words to fully utilize this expended hablife span before tidal locking becomes a problem.

In any playing around with the parameters K0/0.45 Lsol was never a problem, always fully utilizing its long hablife span (est. 9 – 10 gy) before tidal locking.

So this seems to confirm that the ‘optimal’ stars from point of view of long hablife span may indeed be from later G (about G5) to early K (K0/K1, maybe K2), but not much dimmer.

(Note, that this does not take into account any geological factors influencing a planet’s habitable lifespan).

A little addendum (or corrigendum) to my previous post: I should not repeat the same error to which Doug rightly pointed me in another thread, with regard to habitable lifespan:
The habitable lifespan (estimated as some 5.5 gy for the earth) is not a characteristic of a star per se, but of an (earthlike) planet in the (continuous) habitable zone of such a star.
The entire main sequence lifespan of the star will be much more than that, roughly double (about 10 gy for our sun, 12 gy for a typical G5 star of 0.93 Msol/0.80 Lsol, 17 gy for a typical K0 of 0.77 Msol/0.45 Lsol).

As the planet moves out of the CHZ on the inside (or rather, the CHZ moves outward), it is possible that another planet, further out, enters it.

The question is then how fast this ‘within main sequence brightening’ of a solar type star takes place and whether it allows enough time for the more outer planet to start and develop life.

Point remains firmly that anything below about K3/o.20 Lsol/0.5 AU gets tidally locked so quickly that it is hardly worthwhile.

Biological Damage due to Photospheric, Chromospheric and Flare Radiation in the Environments of Main-Sequence Stars

Authors: M. Cuntz, E. F. Guinan, R. L. Kurucz

(Submitted on 10 Nov 2009)

Abstract: We explore the biological damage initiated in the environments of F, G, K, and M-type main-sequence stars due to photospheric, chromospheric and flare radiation. The amount of chromospheric radiation is, in a statistical sense, directly coupled to the stellar age as well as the presence of significant stellar magnetic fields and dynamo activity.

With respect to photospheric radiation, we also consider detailed synthetic models, taking into account millions or hundred of millions of lines for atoms and molecules. Chromospheric UV radiation is increased in young stars in regard to all stellar spectral types.

Flare activity is most pronounced in K and M-type stars, which also has the potential of stripping the planetary atmospheres of close-in planets, including planets located in the stellar habitable zone.

For our studies, we take DNA as a proxy for carbon-based macromolecules, guided by the paradigm that carbon might constitute the biochemical centerpiece of extraterrestrial life forms. Planetary atmospheric attenuation is considered in an approximate manner.

Talk of habitable zones around these earlyK type stars should be tempered with the factor that higher mass worlds can retain thicker insulating atmospheres, and the higher rate of vulcanism on these worlds would add greenhouse gasses to the already thick atmosphere.

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